LOSSY COMPRESSION OF STOCHASTIC HALFTONES WITH JBIG2 Magesh Val liappan and Brian L. Evans Dave A. D. Tompkins and Faouzi Kossentini Dept. of Electrical and Computer Eng. Dept. of Electrical and Computer Eng. The UniversityofTexas at Austin University of British Columbia Austin, TX 78712-1084 USA Vancouver, B.C. V6T 1Z4 Canada fmagesh,b [email protected] fdavet,[email protected] c.ca ibility for enco der designs. An enco der could segment bi- ABSTRACT level images into text, halftone, and generic regions, and The JBIG2 standard supp orts lossless and lossy co ding mo d- enco de each region separately [3, 4]. For halftone regions, els for text, halftone, and generic regions in bi-level im- JBIG2 supp orts very high lossy compression rates. This ages. For the JBIG2 lossy halftone compression mo de, pap er develops a new high-quali ty lossy JBIG2 enco ding halftones are descreened b efore enco ding. Previous JBIG2 metho d tailored for sto chastic halftones. We develop visual descreening implementations pro duce high-quali ty images quality measures, whichwe use for rate-distortion tradeo s. for clustered dot halftones at high compression rates but Weachieve an additional 35 compression over the b est re- signi cantly degrade the image quality for sto chastic half- p orted metho d [5]. We implement the metho d in the JBIG2 tones, even at muchlower rates. In this pap er, we develop co dec available at http://spmg.ece.ubc.ca/jbig2. 1 a exible, computational ly ecient, JBIG2-compliant metho d for compressing sto chastic halftones that reduces 2. BACKGROUND noise, artifacts, and blurring; 2 quality measures for lin- ear and nonlinear distortion in compressed halftones; and JBIG2 uses a form of vector quantization for compressing 3 rate-distortion tradeo s for the enco der parameters. halftones. First, the enco der descreens inverse halftone the bi-level image into a grayscale image with reduced spa- 1. INTRODUCTION tial resolution. Gray levels serve as indices into a halftone pattern dictionary, whichischosen by the enco der. Then, Digital halftoning converts a continuous-tone image into a the enco der enco des the halftone pattern dictionary and bi-level image halftone for printing and display on binary grayscale image bitplanes losslessly using the generic mo de devices. Bi-level images consist of a single rectangular bit of op eration, and cho oses the orientation for the halftoning plane. Pixels are either assigned black or white to create grid. The deco der rst deco des the bitplanes to construct an illusio n of continuous shades of gray. the grayscale image and then constructs the bi-level im- Halftoning by ordered dithering thresholds a grayscale age by placing the dictionary patterns corresp onding to the image by using a p erio dic mask of threshold values. In grayscale values at their appropriate p ositions and orienta- clustered dot ordered dithering, black dots are clustered tions. Thus, the spatial resolution and numb er of gray levels in large blobs. Since clustered dot halftones are resistant directly a ect the quality and compression ratio. Perceptu- to ink spread, they are the most common among printed ally lossless compression is achieved by preserving the lo cal halftones. Sto chastic halftoning varies the thresholding ac- average gray level but not the bi-level image itself. cording to lo cal statistics in the image in order to shap e One descreening metho d [5] maps each non-overlappin g the quantization noise into the high frequencies where the M M window of halftone pixels to one grayscale pixel human visual system is less sensitive. Sto chastic halfton- value that is equal to the numb er of black pixels in the ing requires more computation and generally yields b etter halftone window. For non-angled grids, this metho d yields 2 visual quality than ordered dithering [1]. M + 1 gray levels. For angled grids, a mask is used with Current fax machines only supp ort one lossless com- the window so that adjacent patterns do not overlap, and 2 pression mo de that has b een optimized for textual data [2] the numberofgray levels is area of the mask +1 M +1. and causes data expansion when applied to halftones. The This metho d is conceptually and computationall y simple, Joint Bi-Level Exp erts Group JBIG is a sub committee of and works well for ordered dithered halftones. When this b oth the ISO/IEC and the ITU-T that is developing a sec- metho d is applied to sto chastic halftones, the grayscale im- ond international standard for bi-level image compression age su ers from noise, blur, and artifacts, which degrade for use in printers, fax machines, scanners, and do cument the reconstructed halftone quality[5]. storage and archiving. JBIG2 adds lossy compression and For sto chastic halftones, inverse halftoning metho ds in supp orts several di erent co ding mo dels for text, halftone descending order of quality are set theoretic [10], nonlinear and generic regions. JBIG2 should b e nalized in Fall 1999. denoising [7], adaptive smo othing [6], overcomplete wavelet JBIG2 sp eci es the bit stream syntax, which places expansion [8], wavelet denoising [9], pro jection onto convex strict requirements on deco der designs but leaves much ex- sets [11], and vector quantization [12]. The inverse halftones have the same spatial resolution as the halftone but with M. Valliappan and B. Evans were supp orted by a US Na- 6{8 bits of precision p er pixel. For higher compression, tional Science Foundation CAREER Award under grant MIP- a JBIG2 enco der would create a grayscale image at lower 9701707. D. Tompkins and F. Kossentini were supp orted by the spatial resolution and fewer gray levels. Natural Sciences and Engineering Research Council of Canada. 3. PROPOSED ENCODING METHOD 4. QUALITY METRICS We develop quality metrics to evaluate the p erformance The prop osed enco der in Fig. 1 takes a sto chastic halftone of the prop osed enco ding metho d. The prop osed enco d- as input and generates a JBIG2-compliant bitstream as out- ing metho d attempts to preserve the useful information put. The free parameters are grid size and orientation, num- present in the sto chastic halftone while discarding as much b er of quantization levels, and sharp ening control. noise and distortion as p ossible. So, we compare the input The pre lter should suppress high-frequency noise, spu- halftone with the original grayscale image. rious tones, and Nyquist frequencies in sto chastic halftones, Signal to noise ratios SNRs assume that the only source and it should have a at passband resp onse to minimize of degradation in a pro cessed signal is additive noise. Com- distortion [13]. To meet these criteria while maintaining pression and halftoning also intro duce linear and nonlinear computational simplicity,we design a symmetric 3 3 - distortion. Because the human visual system resp onds in- nite impulse resp onse lter with p ower-of-two co ecients " 1 2 1 dep endently to linear distortion and noise, we develop a [13]: 2 4 2 . The pre lter pro duces a grayscale image quality measure for each e ect [13 , 18]. We quantify the 1 2 1 linear distortion by constructing a minimum mean squared at the same spatial resolution as the halftone. error Weiner lter so that the residual image is uncorre- The decimator consists of a lowpass anti-aliasing lter lated with the input image. The residual image represents followed bydownsampling by M in each dimension. The the nonlinear distortion plus additive indep endent noise. lter sums the pixel intensities within the pattern mask. To quantify the e ect of nonlinear distortion and noise For unangled grids, this corresp onds to a cuto frequency on quality,we sp ectrally weight the residual by a contrast of in each dimension. This pro cess is very similar to sensitivity function CSF. A CSF is a linear approximation M [5] except that the mask and the window are applied to of the human visual system resp onse to a sine waveofa the ltered grayscale values instead of the bi-level image single frequency [13, 18]. A lowpass CSF assumes that the and that the numb er of resulting gray levels is signi cantl y observer do es not fo cus on one p oint in the image but freely higher. In our implementation , we combine the pre lter moves the eyes around the image. We form a weighted SNR and the anti-aliasin g lter. Since the input would b e a bi- P P 2 jX u; v C u; v j level image, we replace multiplicati ons with additions. For u v P P WSNR = 10 log 10 2 a33 smo othing lter and a window size of M M ,we jD u; v C u; v j u v 2 need at most M +2 additions for each grayscale value. 2 The quantizer uses N gray levels N M + 1. Con- where C u; v isalowpass CSF, and X u; v and D u; v ventional quantization with 32 or fewer levels M 5 are the Fourier transforms of windowed original and residual would create false contours [14]. Toavoid contouring, we images, resp ectively. A higher WSNR means higher quality. dither the input image using a multi-level version [15 ] of To prevent WSNRs to b e biased by large DC comp onents, mo di ed error di usion [16]. Error di usion, whichisa we initiall y remove the DC comp onent of the images. typ e of 2-D sigma-delta mo dulation, shap es the quantiza- To quantify the e ect of linear distortion, we compute tion noise into the higher frequencies.